integral 4 sin 5x sin x dx integral cos 3x cos x dx integral 3 sin 2x dx
1. integral 4 sin 5x sin x dx integral cos 3x cos x dx integral 3 sin 2x dx
= integral 2 (sin6x+cos4x) dx , integral 1/2(cos4x +cos 2x) dx, 3 integral sin2x dx
2. integral 4 sin 5x cos 3x dx adalah
int 4 sin(5x) cos(3x) dx
= int 2 (2sin(5x)cos(3x) dx
= 2 int (sin(5x+3x) + sin(5x-3x)) dx
= 2 int (sin(8x) + sin(2x)) dx
= 2 (-1/8 cos(8x) - 1/2 cos(2x)) + C
= -1/4 cos(8x) - cos(2x) + C
3. integral dari 4 sin 5x cos 3x dx
int (4 sin 5x cos 3x) dx
= int (2 . 2 sin 5x cos 3x) dx
= int (2 (sin 8x + sin 2x) dx
= int (2sin8x + 2sin 2x) dx
= -2/8 cos 8x - 2/2 cos 2x + C
= (-1/4) cos 8x - cos 2x + C[tex] \int\limits {4 sin 5x cos 3x} \, dx \\ = \int\limits {4( \frac{1}{2} (sin (5x+3x)+sin(5x-3x) ))} \, dx \\ = \int\limits {2 sin(8x)+sin(2x)}\, dx \\ = \int\limits {2 sin(8x)} \ + \int\limits { sin(2x)} \\ = 2\int\limits {sin(8x)} \ + \int\limits { sin(2x)} \\ =2(- \frac{1}{8} cos8x)+ ( -\frac{1}{2}cos2x) +c\\ =(- \frac{1}{4} cos8x)+ (-\frac{1}{2}cos2x) +c\\ = -\frac{cos8x}{4} -\frac{2cos2x}{4} + c\\ =-\frac{cos8x+2cos2x}{4} + c[/tex]
4. Integral 2 sin 5x cos 3x dx = ....
Gunakan rumus 2.Sin A.Cos B = Sin (A+B) + Sin (A-B)
= ∫2.Sin 5x.Cos 3x dx
= ∫ Sin 8x + Sin 2x dx
= - 1/8.Cos 8x - 1/2.Cos 2x + c
___ selesai ___
5. tentukan hasil integral dari trigonometri berikut : 1. integral sin (4x - 2 ) dx 2. integral 6 cos 4x dx 3. integral (5 sin x - cos (4 - 3x)) dx 4. integral (cos 3x - 2 sin 2x ) dx 5. integral 15 sin 2x cos 3x dx 6. integral cos 4x cos 2x dx 7. integral (sin 7x cos 3x ) dx
nomer 1
integral sin (4x - 2 ) dx
= -1/4.cos (4x - 2) + C
nomer 2
integral 6 cos 4x dx
= -3/2.sin 4x + C
nomer 3
integral (5 sin x - cos (4 - 3x)) dx
= -5.cos x + 1/3.sin (4 - 3x) + C
nomer 4
integral (cos 3x - 2 sin 2x ) dx
= 1/3.sin 3x + cos 2x + C
nomer 5
integral 15 sin 2x cos 3x dx
= integral 15/2.(2. sin 2x cos 3x) dx
= integral 15/2.(sin (5/2)x + sin (-1/2)x) dx
= integral 15/2.sin (5/2)x + 15/2.sin (-1/2)x) dx
= -3.cos (5/2)x +15.cos (1/2)x + C
nomer 6
integral cos 4x cos 2x dx
= integral 1/2.(2.cos 3x + 2.cos x)dx
= integral (cos 3x + cos x)dx
= 1/3.sin 3x + sin x + C
nomer 7
integral (sin 7x cos 3x ) dx
= integral 1/2.(2.sin 7x cos 3x ) dx
= integral 1/2.(sin 5x + sin 2x) dx
= integral (1/2.sin 5x + 1/2.sin 2x) dx
= -1/10.cos 5x -1/4.cos 2x + C
6. Integral cos 5x sin 3x dx
.maaf kalau salah.
Dengan aturan penjumlahan dan selisih sudut, akan diperoleh:
cos A . cos B = 1/2 {cos(A+B) + cos(A-B)}
Sehingga:
cos 5x . cos 3x
= 1/2 [cos(5x+3x) + cos(5x-3x)]
= 1/2 [cos 8x + cos 2x]
Dengan integralnya adalah:
∫ cos 5x.cos 3x dx
= ∫ 1/2 (cos 8x + cos 2x) dx
= 1/2 ∫ (cos 8x + cos 2x) dx
Mengingat:
∫ cos ax dx = 1/a sin ax + C
Menghasilkan:
= 1/2 (1/8 sin 8x + 1/2 sin 2x) + C
= 1/16 sin 8x + 1/4 sin 2x + C
7. integral 8 sin 5x cos 3x dx
∫ 8 sin 5x cos 3x dx
∫ 4 ( 2 sin 5x cos 3x) dx
4 ∫ sin 8x + sin 2x dx
= 4 (- 1/8 cos 8x - 1/2 cos 2x ) + c
= - 1/2 cos 8x - 2 cos 2x + c
8. Integral 6 sin 5x cos 3x dx
semoga membantu yaa :)2 sin 5x cos 3x = sin 8x + sin 2x
∫6 sin 5x cos 3x dx
= 3 ∫2 sin 5x cos 3x dx
= 3 ∫(sin 8x + sin 2x) dx
= 3 ( -1/8 ∫dcos 8x - 1/2 ∫dcos 2x)
= 3 (-1/8 cos 8x - 1/2 cos 2x) + C
= -3/8 cos 8x - 3/2 cos 2x + C
9. tentukan integral fungsi integral (sin 5x+cos 3x)dx
ini jawabannyaaaaaaaa0
10. 1. integral 2 sin 5x cos 3x dx adalah? 2. integral cos 7x cos 3x dx adalah? 3. integral sin^4 2x cos 2x dx adalah? 4. integral tan x sec x dx adalah? bantu ya beserta caranya:)
Kategori soal : matematika
Kelas : 12 SMA
Materi : integral
Kata kunci : sifat integral
Pembahasan : perhitungan terlampir
11. tentukan hasil integral dari trigonometri berikut : 1. integral sin (4x - 2 ) dx 2. integral 6 cos 4x dx 3. integral (5 sin x - cos (4 - 3x)) dx 4. integral (cos 3x - 2 sin 2x ) dx 5. integral 15 sin 2x cos 3x dx 6. integral cos 4x cos 2x dx 7. integral (sin 7x cos 3x ) dx
Kalo kurang jelas tanya aja. Semoga membantu.
12. hasil integral 4 sin 5x cos 3x dx=
Jawab:
Penjelasan dengan langkah-langkah:
sin A cos B = 1/2 (sin (A+B) + sin (A-B))
∫4sin 5x cos 3x dx =∫ 4/2 (sin (5x+3x) + sin (5x-3x))dx
=∫2 sin 8x dx+ 2 ∫sin 2x dx
= 2. 1/8 (-cos 8x) +2/(-1/2) cos2 x+C
=-1/4 cos 8x - cos 2x +C
jawaban B
13. Integral 2 sin 5x cos 3x dx
Untuk integral ini, ada alternatif:
[tex]\boxed{2\cos A\cos B=\cos(A+B)+\cos(A-B)}[/tex]
Maka integral berikut berubah menjadi:
[tex]$\begin{align}\int 2\sin5x\cos3x\, dx&=\int\cos(5x+3x)+\cos(5x-3x)\, dx \\ &=\int \cos8x+\cos2x\, dx \\ \text{Dengan : }&\int \cos ax\, dx=\frac1a\sin ax+C \\ &=\frac18\sin8x+\frac12\sin2x+C \\ &=\frac18(\sin8x+4\sin2x)+C \end{align}[/tex]
14. integral 4 sin 5x cos 3x dx
kita rubah dulu
4 sin 5x cos 3x=2(2sin 5x cos 3x)
=2(sin (5x+3x)+sin(5x-3x)
=2(sin8x+sin3x)
2sin8x+2sin3x
int4sin5xcos 3x
int(2sin 8x+2sin3x)
int(2sin8x)+int(2sin3x)
2/8cos8x+⅔cos 3x +c
¼ cos 8x +⅔ cos 3x+c
15. Selesaikan tiap integral dibawah ini menggunakan rumus--rumus triginometri. A. Integral 2 sin 5x cos 3x dx B. Integral 2 cos 3 x sin x dx C. Integral cos 7x cos 3x dx D. Integral 4 sin 2x sin x dx
a) int 2{½sin(5x+3x)+sin(5x-3x)}dx
int 2{½(sin 8x+sin 2x)}dx
2{-⅛cos8x-½cos2x}+C
2(-1/16cos8x-¼cos2x)+C
-1/8cos8x-½cos2x+C
cmiiw.
16. Selesaikan tiao integral dibawah ini menggunakan rumus-rumud trigonimetri. A. Integral 2 sin 5x cis 3x dx B. Integral 2 cos 3x sin x dx C. Integral cos 7x cos 3x dx D. Integral 4 sin 2x sun x dx
A kalogak sallllllllllllllllah
17. nilai dari integral sin 5x cos 3x dx
Int (sin 5x cos 3x) dx
= Int 1/2 (sin (5x+3x) + sin (5x-3x)) dx
= Int (1/2 sin 8x + 1/2 sin 2x) dx
= -1/16 cos 8x - 1/4 cos 2x + C
18. Integral cos 5x sin 3x dx
Pake identitas trigon
19. integral 8 sin 5x cos 3x dx
int 8 sin(5x)cos(3x) dx
= 4 int 2 sin(5x) cos(3x) dx
= 4 int (sin(5x + 3x) + sin(5x - 3x)) dx
= 4 int (sin(8x) + sin(2x)) dx
= 4 (-1/8 cos(8x) - 1/2 cos(2x)) + c
= - 1/2 cos(8x) - 2 cos(2x) + c
20. Selesaikan integral tak tentu fungsi trigonometri berikut ini! a. Integral 2 sin 4x cos 2x dx b. Integral 4 sin 5x sin x dx c. Integral cos 3x cos x dx
semoga membantu jawaban dilampirkan
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